Products of involutions over fields

Abstract

We consider matrices in the group ± SL(n,F) of all invertible n x n matrices of determinant ± l with entries over the field F that can be written as the product of involutions, and we show that any such matrix can be written as the product of at most four involutions. We also consider special cases of matrices in this group that can be written as the product of exactly two or three involutions, and we show how this concept of factoring a matrix into a product of involutions can be extended to special classes of rings that are not fields.